4. Construct truth tables for the compound propositions: a) (p→ q) V – (p → q) b) (p V - q) A (q V -p) с) (р^-9) —R d) (р — q) л(р — R) 5. Show that (¬ p V q) → ((p ^ ¬q) is a tautology. 6. Use the laws of propositional logic to show that: a) (p V q) ^ ¬q="p^q b) (-pV q) → (p A q) = P c) pA (-p→ q) = P (Note not use Truth Table) 7. Test the validity of the following arguments by constructing truth tables: a) If it rains, Joe will be sick Joe was not sick : It did not rain b) Either you study or you play You do not study (exclusiv : You play 8. Prove that the sum of an even umber and an odd number is odd. 9. Suppose X is an integer. Prove that if 2X+3 is odd, then X is odd. 10. Suppose n us an integer. Prove that if n +5 is number odd, then n is even 11. Prove that the of product of 2 even integer is even. 12. Prove that V3 is irrational.

Q: Show that [~q a (p → q)] →►p is tautology by constructing truth table.

A: We know that A tautology is a compound statement in Maths which always results in Truth value. and…

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A:

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Q: Let x, y, z ∈ { 0, 1 } be bits, and let ϕ be the logical expression ϕ(x,y,z) = (x ⇒ y) AND ((y AND…

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A:

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A:

Q: Give at least two (2) examples that illustrate the different forms of propositions.

A: Propositions are declarative statements that are either true or false.

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A:

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